{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "fec29d82-8692-4ae2-8743-7a81049dda8a",
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib as mpl\n",
    "from tqdm import tqdm\n",
    "import time\n",
    "import seaborn as sns\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pylab as plt\n",
    "from scipy.interpolate import interp1d\n",
    "from scipy.special import ellipj\n",
    "from scipy.special import ellipkinc\n",
    "from scipy.optimize import fsolve"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "ff8b16de-092a-421d-8441-34c52785b6ef",
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rc('text', usetex=True)\n",
    "plt.rc('font', family='serif')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "eea48b4b-af8d-44c9-bbe3-6a49e7ebc3cb",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = 1 # massa do BURACO negro\n",
    "b_c = 3*np.sqrt(3)*M # parametro de impacto CRITICO\n",
    "theta_0 = 85*np.pi/180. #angulo de visada do buraco negro\n",
    "\n",
    "def B_fun(p):\n",
    "    return (p**3/(p-2*M))**0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "id": "2d623cc1-46d7-4f11-8a31-007b1adf9fa8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "85.0"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_0*180/np.pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "8134efe5-5178-42c5-9601-a757db511b71",
   "metadata": {},
   "outputs": [],
   "source": [
    "def Q_fun(P):    \n",
    "    return ((P - 2*M)*(P+6*M))**0.5\n",
    "\n",
    "\n",
    "def gamma(alpha, theta_0):\n",
    "    a = np.cos(alpha)**2 + 1/(np.tan(theta_0)**(2))\n",
    "    return np.arccos( np.cos(alpha)/(a**0.5)  )\n",
    "\n",
    "\n",
    "def k2(P):\n",
    "   \n",
    "    Q = Q_fun(P)\n",
    "    return ((Q-P+6*M)/(2*Q))\n",
    "\n",
    "def zeta_inf(P):\n",
    "    Q = Q_fun(P)\n",
    "    ratio = (Q-P+2*M)/(Q-P +6*M)\n",
    "    return np.arcsin( ratio**0.5 )\n",
    "\n",
    "def Up(P,alpha): #u = 1/r\n",
    "    # b = np.sqrt(X**2 + Y**2)\n",
    "    # alpha = np.arctan(Y/X)\n",
    "    Q = Q_fun(P)\n",
    "    A1 = (Q-P+2*M)/(4*M*P)\n",
    "    A2 = (Q-P+6*M)/(4*M*P)\n",
    "    g = gamma(alpha,theta_0)\n",
    "    ratio = (Q/P)**0.5\n",
    "    mod = k2(P)\n",
    "    sn, cn, dn, ph = ellipj( ((g/2)*ratio + ellipkinc(zeta_inf(P) , mod)), mod )\n",
    "    \n",
    "    return -A1 + A2*sn**2 #tenho de procurar jacobi porra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "id": "8943e2d1-8fa6-4ba4-9513-480b9daa2399",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "52it [01:04,  1.24s/it]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (8,8))\n",
    "#r_list = [30*M,20*M,10*M,6*M]\n",
    "r_list = np.arange(4,30,0.5)*M\n",
    "\n",
    "for idx, r in tqdm(enumerate(r_list)):\n",
    "    alpha_list = np.arange(0, 2*np.pi,0.01)\n",
    "    b_list = []\n",
    "    alpha_res = []\n",
    "    #plt.figure(figsize = (15,15), dpi = 300)\n",
    "    for alpha in alpha_list:    \n",
    "        def cu(P):\n",
    "            return 1 - r*Up(P,alpha)\n",
    "        \n",
    "        #P_list = np.arange(3*M, 50*M,0.1)\n",
    "        \n",
    "        #plt.plot(P_list, cu(P_list))\n",
    "        \n",
    "        guess = b_c + 0.1\n",
    "        raiz = fsolve(cu,[guess])[0]\n",
    "        if raiz != guess:\n",
    "        \n",
    "            #plt.scatter(raiz, cu(raiz))\n",
    "            \n",
    "            b_raiz = B_fun(raiz)\n",
    "            b_list.append(b_raiz)\n",
    "            alpha_res.append(alpha)\n",
    "            \n",
    "        # raiz = fsolve(cu,[4])[0]\n",
    "        \n",
    "        # #plt.scatter(raiz, cu(raiz))\n",
    "        \n",
    "        # b_raiz = B_fun(raiz)\n",
    "        # b_list.append(b_raiz)\n",
    "        \n",
    "        #print(\"b raiz = \", b_raiz)\n",
    "    #plt.plot(P_list, 0*np.ones(P_list.size), linestyle = 'dashed', color = 'black')\n",
    "    #plt.show()\n",
    "    \n",
    "    x = b_list*np.cos(alpha_res)\n",
    "    y = b_list*np.sin(alpha_res)\n",
    "    \n",
    "    if idx > 3:\n",
    "        x_interp = np.concatenate((y[-20:-10], y[10:20]))\n",
    "        y_interp = np.concatenate((-x[-20:-10], -x[10:20]))\n",
    "        f = interp1d(x_interp, y_interp, kind = 'quadratic')\n",
    "\n",
    "        x_new = np.linspace(y[-10], y[10], 100)\n",
    "        plt.plot(x_new, f(x_new), color = sns.color_palette('hot_r', len(r_list))[idx],\n",
    "                    zorder = 2, lw = 4)\n",
    "    \n",
    "    plt.plot(y,-x, color = sns.color_palette('hot_r', len(r_list))[idx],\n",
    "            zorder = 2, lw = 4)\n",
    "\n",
    "# x_ovo = 3*M*np.cos(alpha_list)\n",
    "# y_ovo = 3*M*np.sin(alpha_list)\n",
    "circle = plt.Circle((0., 0.), 2*M, color='black', fill=True, zorder=1)\n",
    "plt.gca().add_patch(circle)\n",
    "circle = plt.Circle((0., 0.), 3*M, color='black', fill=True, zorder=1, alpha = 0.3)\n",
    "plt.gca().add_patch(circle)\n",
    "circle = plt.Circle((0., 0.), np.sqrt(3)*3*M, facecolor = 'none', edgecolor='white', fill=True,\n",
    "                    zorder=1, lw = 4)\n",
    "plt.gca().add_patch(circle)\n",
    "\n",
    "plt.xlim(-32,32)\n",
    "plt.ylim(-32,32)\n",
    "plt.axis('off')\n",
    "fig.patch.set_color('dimgrey')\n",
    "for ax in fig.axes:\n",
    "    ax.patch.set_color('dimgrey')\n",
    "plt.title(f'Black hole accretion disk view - {int(theta_0*180/np.pi)}º', fontsize = 20,\n",
    "         color = 'white')\n",
    "# plt.savefig(f'Isoradical_theta_{int(theta_0*180/np.pi)}_mass_{int(M)}.png',\n",
    "#             dpi = 300, bbox_inches = 'tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "id": "1d530e99-6731-4e74-aad3-bed6d930cf37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5.11600435, 5.11653445, 5.11704324, 5.11753115, 5.11799861,\n",
       "       5.11844602, 5.11887377, 5.11928223, 5.11967172, 5.12004259,\n",
       "       5.12039514, 5.12072965, 5.12104642, 5.12134568, 5.1216277 ,\n",
       "       5.12910645, 5.1356851 , 5.14409464, 5.15059438, 5.15688078,\n",
       "       5.15883034, 5.15262232, 5.14618511, 5.13793833, 5.13111941,\n",
       "       5.12171394, 5.12143738, 5.12114363, 5.12083247, 5.12050363,\n",
       "       5.12015686, 5.11979186, 5.11940833, 5.11900596, 5.11858439,\n",
       "       5.11814328, 5.11768225, 5.11720089, 5.11669881, 5.11617555])"
      ]
     },
     "execution_count": 84,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_interp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "1437f538-9b3e-40f4-878b-2eb89bef094b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_interp = np.concatenate((y[-20:-10], y[10:20]))\n",
    "y_interp = np.concatenate((-x[-20:-10], -x[10:20]))\n",
    "f = interp1d(x_interp, y_interp, kind = 'quadratic')\n",
    "plt.plot(y,-x, color = sns.color_palette('hot_r', len(r_list))[idx],\n",
    "            zorder = 2, lw = 4)\n",
    "\n",
    "x_new = np.linspace(y[-10], y[10], 100)\n",
    "plt.plot(x_new, f(x_new), color = 'blue',\n",
    "            zorder = 2, lw = 4)\n",
    "# plt.ylim(-6,-4)\n",
    "# plt.xlim(-10, 10)\n",
    "# plt.savefig('camisinha.png')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b1139e32-c7d1-4caa-87b9-cb462a2e048b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def IsoRadical(r):\n",
    "    alpha_list = np.arange(0, 2*np.pi,0.01)\n",
    "    b_list = []\n",
    "    alpha_res = []\n",
    "    #plt.figure(figsize = (15,15), dpi = 300)\n",
    "    for alpha in alpha_list:    \n",
    "        def cu(P):\n",
    "            return 1 - r*Up(P,alpha)\n",
    "        \n",
    "        #P_list = np.arange(3*M, 50*M,0.1)\n",
    "        \n",
    "        #plt.plot(P_list, cu(P_list))\n",
    "        \n",
    "        guess = b_c + 0.1\n",
    "        raiz = fsolve(cu,[guess])[0]\n",
    "        if raiz != guess:\n",
    "        \n",
    "            #plt.scatter(raiz, cu(raiz))\n",
    "            \n",
    "            b_raiz = B_fun(raiz)\n",
    "            b_list.append(b_raiz)\n",
    "            alpha_res.append(alpha)\n",
    "            \n",
    "        # raiz = fsolve(cu,[4])[0]\n",
    "        \n",
    "        # #plt.scatter(raiz, cu(raiz))\n",
    "        \n",
    "        # b_raiz = B_fun(raiz)\n",
    "        # b_list.append(b_raiz)\n",
    "        \n",
    "        #print(\"b raiz = \", b_raiz)\n",
    "    #plt.plot(P_list, 0*np.ones(P_list.size), linestyle = 'dashed', color = 'black')\n",
    "    #plt.show()\n",
    "    \n",
    "    x = b_list*np.cos(alpha_res)\n",
    "    y = b_list*np.sin(alpha_res)\n",
    "    \n",
    "    return x,y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "id": "7d033930-dfff-4fc1-80b7-66504c655c8d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/html": [
       "<div style=\"vertical-align: middle;\"><strong>hot</strong> </div><div class=\"cmap\"><img alt=\"hot colormap\" title=\"hot\" style=\"border: 1px solid #555;\" src=\"\"></div><div style=\"vertical-align: middle; max-width: 514px; display: flex; justify-content: space-between;\"><div style=\"float: left;\"><div title=\"#0b0000ff\" style=\"display: inline-block; width: 1em; height: 1em; margin: 0; vertical-align: middle; border: 1px solid #555; background-color: #0b0000ff;\"></div> under</div><div style=\"margin: 0 auto; display: inline-block;\">bad <div title=\"#00000000\" style=\"display: inline-block; width: 1em; height: 1em; margin: 0; vertical-align: middle; border: 1px solid #555; background-color: #00000000;\"></div></div><div style=\"float: right;\">over <div title=\"#ffffffff\" style=\"display: inline-block; width: 1em; height: 1em; margin: 0; vertical-align: middle; border: 1px solid #555; background-color: #ffffffff;\"></div></div>"
      ],
      "text/plain": [
       "<matplotlib.colors.LinearSegmentedColormap at 0x7fa4a0d74e90>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mpl.cm.hot#(norm = mpl.colors.PowerNorm(gamma=0.5))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "3fa534e9-028b-47e0-ac51-4108fe511c00",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 4/4 [04:24<00:00, 66.00s/it]\n"
     ]
    }
   ],
   "source": [
    "for angle in tqdm([5*i for i in range(15,19)]):\n",
    "    M = 1 # massa do BURACO negro\n",
    "    b_c = 3*np.sqrt(3)*M # parametro de impacto CRITICO\n",
    "    theta_0 = angle*np.pi/180. #angulo de visada do buraco negro\n",
    "\n",
    "    fig, ax = plt.subplots(figsize = (8,8))\n",
    "    #r_list = [30*M,20*M,10*M,6*M]\n",
    "    r_list = np.arange(4,30,0.5)*M\n",
    "\n",
    "    for idx, r in enumerate(r_list):\n",
    "        if angle > 82:\n",
    "            alpha_list = np.arange(0, 4*np.pi,0.01)\n",
    "        else:\n",
    "            alpha_list = np.arange(0, 2*np.pi,0.01)\n",
    "        b_list = []\n",
    "        alpha_res = []\n",
    "        #plt.figure(figsize = (15,15), dpi = 300)\n",
    "        for alpha in alpha_list:    \n",
    "            def cu(P):\n",
    "                return 1 - r*Up(P,alpha)\n",
    "\n",
    "            #P_list = np.arange(3*M, 50*M,0.1)\n",
    "\n",
    "            #plt.plot(P_list, cu(P_list))\n",
    "\n",
    "            guess = b_c + 0.1\n",
    "            raiz = fsolve(cu,[guess])[0]\n",
    "            if raiz != guess:\n",
    "\n",
    "                #plt.scatter(raiz, cu(raiz))\n",
    "\n",
    "                b_raiz = B_fun(raiz)\n",
    "                b_list.append(b_raiz)\n",
    "                alpha_res.append(alpha)\n",
    "\n",
    "            # raiz = fsolve(cu,[4])[0]\n",
    "\n",
    "            # #plt.scatter(raiz, cu(raiz))\n",
    "\n",
    "            # b_raiz = B_fun(raiz)\n",
    "            # b_list.append(b_raiz)\n",
    "\n",
    "            #print(\"b raiz = \", b_raiz)\n",
    "        #plt.plot(P_list, 0*np.ones(P_list.size), linestyle = 'dashed', color = 'black')\n",
    "        #plt.show()\n",
    "\n",
    "        x = b_list*np.cos(alpha_res)\n",
    "        y = b_list*np.sin(alpha_res)\n",
    "        \n",
    "        if angle < 82:\n",
    "            if idx > 2:\n",
    "                x_interp = np.concatenate((y[-20:-10], y[10:20]))\n",
    "                y_interp = np.concatenate((-x[-20:-10], -x[10:20]))\n",
    "                f = interp1d(x_interp, y_interp, kind = 'quadratic')\n",
    "\n",
    "                x_new = np.linspace(y[-10], y[10], 100)\n",
    "                plt.plot(x_new, f(x_new), color = sns.color_palette('hot_r', len(r_list))[idx],\n",
    "                            zorder = 2, lw = 4)\n",
    "\n",
    "        plt.plot(y,-x, color = sns.color_palette('hot_r', len(r_list))[idx],\n",
    "                zorder = 2, lw = 4)\n",
    "\n",
    "    # x_ovo = 3*M*np.cos(alpha_list)\n",
    "    # y_ovo = 3*M*np.sin(alpha_list)\n",
    "    circle = plt.Circle((0., 0.), 2*M, color='black', fill=True, zorder=1)\n",
    "    plt.gca().add_patch(circle)\n",
    "    circle = plt.Circle((0., 0.), 3*M, color='black', fill=True, zorder=1, alpha = 0.3)\n",
    "    plt.gca().add_patch(circle)\n",
    "    circle = plt.Circle((0., 0.), np.sqrt(3)*3*M, facecolor = 'none', edgecolor='white', fill=True,\n",
    "                        zorder=1, lw = 3)\n",
    "    plt.gca().add_patch(circle)\n",
    "\n",
    "    plt.xlim(-32,32)\n",
    "    plt.ylim(-32,32)\n",
    "    plt.axis('off')\n",
    "    fig.patch.set_color('dimgrey')\n",
    "    for ax in fig.axes:\n",
    "        ax.patch.set_color('dimgrey')\n",
    "    plt.title(f'Black hole accretion disk view - {int(theta_0*180/np.pi)}º', fontsize = 20,\n",
    "             color = 'white')\n",
    "    plt.savefig(f'Isoradical_theta_{int(theta_0*180/np.pi)}_mass_{int(M)}.png',\n",
    "                dpi = 300, bbox_inches = 'tight')\n",
    "    plt.savefig(f'Isoradical_theta_{int(theta_0*180/np.pi)}_mass_{int(M)}.svg',\n",
    "                dpi = 300, bbox_inches = 'tight')\n",
    "    plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "27566d7c-2281-4ac9-afa7-2c9352329d74",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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